Legally speaking yes that is all that is required of a sea kayak by COLREGS the international regulations to prevent collisions at sea. Rule 25 requires that vessels propelled by oars only need to show a white light in time to avoid collision.

As someone that has spent a lot of time on the water at night both commercial and recreational I would add that showing running lights and a stern light gives other vessels on the water a better chance to determine the direction of your travel, the type of boat you are in plus the possibility of being seen and avoided before you would feel threatened enough to show your "flareup light"

Mikekayak